Least Common Multiple (LCM) of 110 and 181
The least common multiple (LCM) of 110 and 181 is 19910.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 110 and 181?
First, calculate the GCD of 110 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 181 = 0 remainder 110 |
| 2 | 181 ÷ 110 = 1 remainder 71 |
| 3 | 110 ÷ 71 = 1 remainder 39 |
| 4 | 71 ÷ 39 = 1 remainder 32 |
| 5 | 39 ÷ 32 = 1 remainder 7 |
| 6 | 32 ÷ 7 = 4 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 31 | 124 |
| 149 and 55 | 8195 |
| 61 and 130 | 7930 |
| 145 and 191 | 27695 |
| 169 and 100 | 16900 |